Questions tagged [nonlinear-dynamics]
This tag is for questions relating to nonlinear-dynamics, the branch of mathematical physics that studies systems governed by equations more complex than the linear, $~aX+b~$ form.
486
questions
3
votes
0
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84
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Are two separate limit cycles in a dynamical system possible
In all the examples I've seen before with two limit cycles, the limit cycles are always concentric (there is an unstable point at center, a stable limit cycle on the middle and an unstable limit cycle ...
- 77
1
vote
0
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21
views
Realizing a modified transport equation
Stated somewhat informally, the continuity equation or transport equation $\partial_t\rho_t = -\nabla\cdot(\rho_t v_t)$ describes the evolution of a density where each particle flows along a vector ...
- 610
2
votes
0
answers
51
views
How can I linearize the following equation (Bergman model)? [closed]
I have to linearize the following equation so that I can use the Laplace transform and get the transfer function for the system. The equation is:
$$\frac{dG(t)}{dt}=-p_1 G(t)-p_2 X(t)G(t)+ ....$$
$p_1$...
- 29
0
votes
0
answers
7
views
Generalized alignement index of classic Lorenz system?
I am reading about generalized alignment index (GALIs) as chaos indicator. However, I have been looking around for a while now to see an example of this applied on to the classic Lorenz attractor, but ...
5
votes
1
answer
120
views
Why is this approximate solution correct?
Consider the following differential equation
$$ y''=-y + \alpha y |y|^2, $$
where $y=y(x)$ is complex in general and $\alpha$ is a real constant such that the second term is small compared to $y$ ($||^...
- 331
1
vote
1
answer
73
views
General method for finding invariant subsapces of a nonlinear system
Suppose we are given a system:
$$\dot{x_{1}} = f_{1}(x_{1},...,x_{n})$$
$$...$$
$$\dot{x_{n}} = f_{n}(x_{1},...,x_{n})$$
And are interested in finding subspaces of the vector space that are invariant ...
- 402
2
votes
0
answers
67
views
Example of a buried Julia component of a transcendental meromorphic function.
We know examples of buried Julia components (Definition: A Julia component is called buried if it is not contained in the boundary of any Fatou component) for rational functions. In 1998, McMullen ...
0
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0
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71
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Mathematical theory of plasma
I am working on a heavily mathematically project about plasma. In particular, I want to find references that treat the problem from microscopic models that include relativistic and magnetic effects (...
- 113
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17
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Topological conjugacy of the logistic map at different parameter values
I am wondering whether the dynamical systems generated by the discrete 1 dimensional map $g(x;p) = px(1-x)$ (the logistic map) at different values of $p$ are topologically conjugate.
Of course, this ...
0
votes
0
answers
94
views
What should I prove to show the states lie within a compact set?
I'm trying to prove the local stability of a nonlinear system and got the following inequality.
$
\|x(t)\|\leq c_1\|x(t_0)\|\exp(-c_2(t-t_0))+c_3\epsilon_m\cdots
$(i)
where $c_1, c_2, c_3$ are ...
- 165
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vote
0
answers
58
views
Soft question - Index theory in nonlinear dynamics vs Complex analysis
The video https://www.youtube.com/watch?v=wZvFKcQ_3Rc&t=8s mentioned something called the Index Theory. I can't find it on wikipedia. Where could I find more about the theory?
Here index is just ...
- 451
0
votes
0
answers
51
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nonlinear odes: stabilizing terms in a subcritical pitchfork bifurcation
I am reading through Strogatz's book on nonlinear odes and dynamical systems. One thing that is a little confusing is his description of stabilizing higher order terms to control the dynamics of a ...
- 2,531
0
votes
0
answers
13
views
Dynamical system definition in flat to non-flat spaces
I have a dynamical system given by equality $\frac{d}{dt} \begin{bmatrix} q \\ p \end{bmatrix} = \begin{bmatrix} B p \\ -I(q, p) \end{bmatrix} + \begin{bmatrix} 0 \\ U(q) \end{bmatrix} u$, mechanical,...
- 325
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0
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45
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Stability of normal state in chemostat model
The chemostat model proposed by monod was given by,
$$
\begin{align}
\frac{dx}{dt}&=[K(c)-D]x\\
\frac{dc}{dt}&=D[c_0-c]-\frac1yK(c)x
\end{align}
$$
where $x(t)$ is the population of micro-...
- 701
1
vote
1
answer
70
views
Is there an upper limit on the number of equilibrium points a system of nonlinear odes can have?
I am looking at some introductory material on nonlinear odes, and systems of nonlinear odes. The material is simple enough, but I was trying to figure out what would happen in very high dimensional ...
- 2,531